992:
950:
413:
638:
180:
424:
954:
169:
870:
50:
is in space, expressed as an effective volume in which most of the energy associated with an electromagentic mode is confined. Various expressions may be used to estimate this volume:
1051:
408:{\displaystyle V_{m}={\frac {\int \epsilon |E|^{2}dV}{\rm {{max}(\epsilon |E|^{2})}}}\;\;\;{\rm {{or}\;\;\;V_{m}={\frac {\int (|B|^{2}/\mu )\;dV}{\rm {{max}(|B|^{2}/\mu )}}}}}}
418:
The volume that would be occupied by the mode if its electromagnetic energy density was constant and equal to a weighted average value that emphasises higher energy densities.
810:
708:
60:
732:
684:
660:
738:. For cavities in which the electromagnetic energy is not totally confined within the cavity, modficiations to these expressions may be required.
633:{\displaystyle V_{m}={\frac {(\int |E|^{2}dV)^{2}}{\int |E|^{4}dV}}\;\;\;{\rm {{or}\;\;\;V_{m}={\frac {(\int |B|^{2}dV)^{2}}{\int |B|^{4}dV}}}}}
1322:
1033:
1061:
889:
965:
815:
735:
174:
The volume that would be occupied by the mode if its electromagnetic energy density was constant and equal to its maximum value
959:
925:
742:
43:
905:
1262:
Yoshie, T.; Scherer, A.; Hendrickson, J.; Khitrova, G.; Gibbs, H. M.; Rupper, G.; Ell, C.; Shchekin, O. B.; Deppe, D. G.
54:
The volume over which the electromagnetic energy density exceeds some threshold (e.g., half the maximum energy density)
930:
1026:
1215:"Cavity Q, mode volume, and lasing threshold in small diameter AlGaAs microdisks with embedded quantum dots"
1176:"Proceedings of the American Physical Society: B10. Spontaneous Emission Probabilities at Radio Frequencies"
877:
47:
1214:
42:
The mode volume (or modal volume) of an optical or microwave cavity is a measure of how concentrated the
1353:
1348:
711:
687:
1133:
1171:
1019:
783:
1226:
1096:
873:
1213:
Srinivasan, Kartik; Borselli, Matthew; Painter, Oskar; Stintz, Andreas; Krishna, Sanjay (2006).
693:
1318:
1283:
1244:
1195:
1153:
1114:
1003:
1310:
1275:
1236:
1187:
1145:
1106:
915:
27:
1084:
766:
717:
1302:
935:
920:
910:
746:
669:
663:
645:
31:
23:
1149:
1342:
770:
1175:
969:
758:
1264:"Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity"
1314:
975:
164:{\displaystyle V_{m}=\int \left(|E|^{2}>{\frac {|E_{max}|^{2}}{2}}\right)dV}
1263:
1287:
1248:
1199:
1191:
1157:
1118:
991:
1240:
1110:
1279:
1231:
741:
The mode volume of a cavity or resonator is of particular importance in
749:
and coupling strength between cavity photons and atoms in the cavity.
999:
16:
Number of bound modes that an optical fiber is capable of supporting
1101:
1056:
1134:"Strong Interactions of Single Atoms and Photons in Cavity QED"
894:
which must be greater than 5 for this approximation to be valid
1085:"Generalized effective mode volume for leaky optical cavities"
1083:
Kristensen, P. T.; Van Vlack, C.; Hughes, S. (2012-05-15).
22:
may refer to figures of merit used either to characterise
865:{\displaystyle {V^{2} \over 2}\left({g \over g+2}\right)}
1007:
818:
787:
720:
696:
672:
648:
427:
183:
63:
864:
804:
726:
702:
678:
654:
632:
407:
163:
1309:, Boston, MA: Springer US, pp. 1033–1033,
1052:"Calculating the modal volume of a cavity mode"
1307:Computer Science and Communications Dictionary
1027:
8:
1034:
1020:
535:
534:
533:
522:
521:
520:
346:
292:
291:
290:
279:
278:
277:
1230:
1100:
840:
825:
819:
817:
792:
785:
745:where it determines the magnitude of the
719:
695:
671:
647:
613:
608:
599:
588:
572:
567:
558:
549:
540:
525:
524:
523:
505:
500:
491:
480:
464:
459:
450:
441:
432:
426:
389:
383:
378:
369:
355:
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335:
329:
324:
315:
306:
297:
282:
281:
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265:
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251:
234:
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220:
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197:
188:
182:
138:
133:
120:
111:
108:
99:
94:
85:
68:
62:
1043:
7:
988:
986:
1006:. You can help Knowledge (XXG) by
622:
619:
604:
581:
578:
563:
541:
537:
529:
526:
374:
362:
359:
356:
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347:
320:
298:
294:
286:
283:
256:
241:
238:
235:
14:
1150:10.1238/Physica.Topical.076a00127
990:
953: This article incorporates
948:
966:General Services Administration
926:Cavity quantum electrodynamics
884:is the profile parameter, and
743:cavity quantum electrodynamics
609:
600:
585:
568:
559:
552:
501:
492:
477:
460:
451:
444:
397:
379:
370:
366:
343:
325:
316:
312:
271:
261:
252:
245:
216:
207:
134:
112:
95:
86:
1:
906:Equilibrium mode distribution
805:{\displaystyle V^{2} \over 2}
773:is capable of supporting.
1315:10.1007/1-4020-0613-6_11695
38:In electromagnetic cavities
1370:
985:
931:Cavity perturbation theory
780:is approximately given by
703:{\displaystyle \epsilon }
1301:Weik, Martin H. (2000),
1192:10.1103/PhysRev.69.674.2
878:power-law index profile
765:is the number of bound
664:electric field strength
1132:Kimble, H. J. (1998).
1002:-related article is a
961:Federal Standard 1037C
955:public domain material
866:
806:
728:
704:
680:
656:
634:
409:
165:
44:electromagnetic energy
974: (in support of
867:
807:
736:magnetic permeability
729:
712:electric permittivity
705:
688:magnetic flux density
681:
657:
635:
410:
166:
1241:10.1364/OE.14.001094
1111:10.1364/OL.37.001649
890:normalized frequency
816:
784:
727:{\displaystyle \mu }
718:
694:
670:
646:
425:
181:
61:
1280:10.1038/nature03119
872:, respectively for
1186:(11–12): 674–674.
862:
798:
724:
700:
676:
652:
630:
405:
161:
28:microwave cavities
1324:978-0-7923-8425-0
1274:(7014): 200–203.
1064:on 17 August 2022
1015:
1014:
856:
834:
802:
679:{\displaystyle B}
655:{\displaystyle E}
626:
518:
401:
275:
148:
1361:
1334:
1333:
1332:
1331:
1298:
1292:
1291:
1259:
1253:
1252:
1234:
1210:
1204:
1203:
1168:
1162:
1161:
1129:
1123:
1122:
1104:
1080:
1074:
1073:
1071:
1069:
1060:. Archived from
1048:
1036:
1029:
1022:
994:
987:
979:
973:
968:. Archived from
952:
951:
916:Mandrel wrapping
871:
869:
868:
863:
861:
857:
855:
841:
835:
830:
829:
820:
811:
809:
808:
803:
797:
796:
786:
776:The mode volume
733:
731:
730:
725:
709:
707:
706:
701:
685:
683:
682:
677:
661:
659:
658:
653:
639:
637:
636:
631:
629:
628:
627:
625:
618:
617:
612:
603:
594:
593:
592:
577:
576:
571:
562:
550:
545:
544:
532:
519:
517:
510:
509:
504:
495:
486:
485:
484:
469:
468:
463:
454:
442:
437:
436:
414:
412:
411:
406:
404:
403:
402:
400:
393:
388:
387:
382:
373:
365:
353:
339:
334:
333:
328:
319:
307:
302:
301:
289:
276:
274:
270:
269:
264:
255:
244:
232:
225:
224:
219:
210:
198:
193:
192:
170:
168:
167:
162:
154:
150:
149:
144:
143:
142:
137:
131:
130:
115:
109:
104:
103:
98:
89:
73:
72:
1369:
1368:
1364:
1363:
1362:
1360:
1359:
1358:
1339:
1338:
1337:
1329:
1327:
1325:
1300:
1299:
1295:
1261:
1260:
1256:
1232:physics/0511153
1212:
1211:
1207:
1180:Physical Review
1170:
1169:
1165:
1138:Physica Scripta
1131:
1130:
1126:
1082:
1081:
1077:
1067:
1065:
1050:
1049:
1045:
1041:
1040:
983:
958:
949:
947:
944:
902:
845:
836:
821:
814:
813:
788:
782:
781:
755:
753:In fiber optics
716:
715:
692:
691:
668:
667:
644:
643:
607:
595:
584:
566:
551:
536:
499:
487:
476:
458:
443:
428:
423:
422:
377:
323:
308:
293:
259:
214:
199:
184:
179:
178:
132:
116:
110:
93:
84:
80:
64:
59:
58:
40:
17:
12:
11:
5:
1367:
1365:
1357:
1356:
1351:
1341:
1340:
1336:
1335:
1323:
1293:
1254:
1219:Optics Express
1205:
1174:(1946-06-01).
1172:Purcell, E. M.
1163:
1124:
1089:Optics Letters
1075:
1042:
1039:
1038:
1031:
1024:
1016:
1013:
1012:
995:
981:
980:
972:on 2022-01-22.
943:
940:
939:
938:
936:Quantum optics
933:
928:
923:
921:Purcell effect
918:
913:
911:Mode scrambler
908:
901:
898:
880:fibers, where
860:
854:
851:
848:
844:
839:
833:
828:
824:
801:
795:
791:
754:
751:
747:Purcell effect
723:
699:
675:
651:
624:
621:
616:
611:
606:
602:
598:
591:
587:
583:
580:
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561:
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548:
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531:
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305:
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273:
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263:
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209:
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196:
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153:
147:
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136:
129:
126:
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119:
114:
107:
102:
97:
92:
88:
83:
79:
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71:
67:
56:
55:
39:
36:
32:optical fibers
15:
13:
10:
9:
6:
4:
3:
2:
1366:
1355:
1352:
1350:
1347:
1346:
1344:
1326:
1320:
1316:
1312:
1308:
1304:
1303:"mode volume"
1297:
1294:
1289:
1285:
1281:
1277:
1273:
1269:
1265:
1258:
1255:
1250:
1246:
1242:
1238:
1233:
1228:
1224:
1220:
1216:
1209:
1206:
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1197:
1193:
1189:
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1177:
1173:
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1164:
1159:
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1143:
1139:
1135:
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1125:
1120:
1116:
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1108:
1103:
1098:
1094:
1090:
1086:
1079:
1076:
1063:
1059:
1058:
1053:
1047:
1044:
1037:
1032:
1030:
1025:
1023:
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1017:
1011:
1009:
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977:
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937:
934:
932:
929:
927:
924:
922:
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912:
909:
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903:
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895:
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883:
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875:
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849:
846:
842:
837:
831:
826:
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799:
793:
789:
779:
774:
772:
771:optical fiber
768:
764:
760:
752:
750:
748:
744:
739:
737:
721:
713:
697:
689:
673:
665:
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614:
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506:
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481:
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429:
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416:
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394:
390:
384:
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336:
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303:
266:
248:
229:
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221:
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200:
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1354:Optics stubs
1349:Fiber optics
1328:, retrieved
1306:
1296:
1271:
1267:
1257:
1222:
1218:
1208:
1183:
1179:
1166:
1141:
1137:
1127:
1095:(10): 1649.
1092:
1088:
1078:
1068:13 September
1066:. Retrieved
1062:the original
1057:Ansys Optics
1055:
1046:
1008:expanding it
997:
982:
970:the original
960:
893:
885:
881:
777:
775:
762:
759:fiber optics
756:
740:
734:denotes the
641:
421:
177:
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46:of a single
41:
19:
18:
1225:(3): 1094.
976:MIL-STD-188
763:mode volume
48:cavity mode
20:Mode volume
1343:Categories
1330:2024-09-13
1144:(1): 127.
942:References
874:step-index
1288:0028-0836
1249:1094-4087
1200:0031-899X
1158:0031-8949
1119:0146-9592
1102:1107.4601
722:μ
698:ϵ
597:∫
556:∫
489:∫
448:∫
395:μ
341:μ
310:∫
249:ϵ
204:ϵ
201:∫
78:∫
900:See also
769:that an
888:is the
710:is the
686:is the
662:is the
24:optical
1321:
1286:
1268:Nature
1247:
1198:
1156:
1117:
1000:optics
714:, and
642:where
1227:arXiv
1097:arXiv
998:This
957:from
767:modes
1319:ISBN
1284:ISSN
1245:ISSN
1196:ISSN
1154:ISSN
1115:ISSN
1070:2024
1004:stub
876:and
812:and
106:>
26:and
1311:doi
1276:doi
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